46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
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This paper provides a brief overview of two linear inverse problems concerned with the determination of the Earth’s interior: inverse gravimetry and normal mode tomography. Moreover, a vector spline method is proposed for a combined solution of both problems. This method uses localised basis functions, which are based on reproducing kernels, and is related to approaches which have been successfully applied to the inverse gravimetric problem and the seismic traveltime tomography separately.